Throughout this description various publications are cited as representative of related art. For the sake of simplicity, these documents will be referred by reference numbers enclosed in square brackets, e.g., [x]. A complete list of these publications ordered according to the reference numbers is reproduced in the section entitled “List of references” at the end of the description. These publications are incorporated herein.
Wireless transmission through multiple antennas, also referred to as MIMO (Multiple-Input Multiple-Output) [1]-[2], currently enjoys great popularity because of the demand of high data rate communication from multimedia services. Many applications are considering the use of MIMO to enhance the data rate and/or the robustness of the link.
Among others, a significant example is provided by the next generation of Wireless Local Area Networks (W-LANs), see e.g., the IEEE 802.11n standard [3]. Another candidate application is represented by mobile “WiMax” systems for fixed wireless access (FWA) [4]-[5]. Besides fourth generation (4G) mobile terminals will likely endorse MIMO technology and as such may represent a very important commercial application for the present arrangement.
A current problem in this area is detecting multiple sources corrupted by noise in MIMO fading channels and generating bit soft output information to be passed to an external outer decoder.
The structure and operation of a narrowband MIMO system can be modelled as a linear complex baseband equation:Y=HX+N  (1)where Y is the received vector (size R×1), X the vector of transmitted complex Quadrature Amplitude Modulation (QAM) or Phase Shift Keying (PSK) constellation symbols (size T×1), H is the R×T channel matrix (R and T are the number of receive and transmit antennas, respectively) whose entries are the complex path gains from transmitter to receiver, samples of zero mean Gaussian random variables (RVs) with variance σ2=0.5 per dimension. N is the noise vector of size R×1, whose elements are samples of independent circularly symmetric zero-mean complex Gaussian RVs with variance N0/2 per dimension. S is the complex constellation size. Equation (1) is considered valid per subcarrier for wideband orthogonal frequency division multiplexing (OFDM) systems.
Maximum-A-Posteriori (MAP) detection is desirable to achieve high-performance, as this is the optimal detection technique in presence of additive white Gaussian noise (AWGN) [6]. If Mc is the number of bits per modulated symbol, for every transmitted bit bk, k=1, . . . , T·Mc it computes the a-posteriori probability (APP) ratio conditioned on the received channel symbol vector
Y:
      P    ⁡          (                        b          k                =                  1          |          Y                    )            P    ⁡          (                        b          k                =                  0          |          Y                    )      
Practically, this is commonly handled in the logarithmic domain. Using Bayes' rule the a-posteriori log-likelihood ratios (LLRs) Lp,k are computed as
                              L                      p            ,            k                          =                              ln            ⁢                                          P                ⁡                                  (                                                            b                      k                                        =                                          1                      |                      Y                                                        )                                                            P                ⁡                                  (                                                            b                      k                                        =                                          0                      |                      Y                                                        )                                                              =                      ln            ⁢                                                            ∑                                      X                    ∈                                          S                      +                      k                                                                      ⁢                                                      p                    ⁡                                          (                                              Y                        |                        X                                            )                                                        ⁢                                                            p                      a                                        ⁡                                          (                      X                      )                                                                                                                    ∑                                      X                    ∈                                          S                      -                      k                                                                      ⁢                                                      p                    ⁡                                          (                                              Y                        |                        X                                            )                                                        ⁢                                                            p                      a                                        ⁡                                          (                      X                      )                                                                                                                              (        2        )            where s+k is the set of 2T·Mc−1 bit sequences having bk=1, and similarly s−k is the set of bit sequences having bk=0; pa(X) represent the a-priori probabilities of X. They can be neglected if equiprobable symbols are considered, and in this case (2) reduced to the maximum-likelihood (ML) metric.
This is not true when extrinsic information is output by an outer decoder, i.e., in iterative schemes, after the first detection-decoder stage is performed. The basic idea of combined iterative detection and decoding schemes is that the soft-output decoder and the detector exchange and update extrinsic soft information in an iterative fashion, according to a “turbo” decoding principle, in analogy to the iterative decoders first proposed for the Turbo Codes [7] and the subsequent turbo equalization schemes [8] to mitigate inter-symbol interference (ISI) in time varying fading channels.
A general block diagram of such a system is portrayed in FIGS. 4A and 4B that will be further discussed in the following.
Such schemes correspond to replacing the inner soft-in soft-out (SISO) decoder in [7] by the MIMO soft-out detector, and can be considered a turbo spatial-equalization scheme. They were first introduced in [12] and called “Turbo-BLAST”. Other references of interest in that respect are [13]-[14].
From the MIMO system shown in equation (1) and assuming the Channel State Information (CSI) H at the receiver is known, one has:
      p    ⁡          (              Y        |        X            )        ∝      exp    ⁡          [                        -                      1                          2              ⁢                              σ                N                2                                                    ⁢                                                        Y              -              HX                                            2                    ]      through a proportionality factor that can be neglected when substituted in equation (2) and where σN2=N0/2. Denoting with La,j the LLRs output by the decoder of the j-th bit in the transmitted sequence X, i.e., the a-priori (logarithmic) bit probability information, and considering independent bit in a same modulated symbol, equation (2) can be further developed as:
                              L                      p            ,            k                          =                  ln          ⁢                                                    ∑                                  X                  ∈                                      S                    +                    k                                                              ⁢                              exp                (                                                                            -                                              1                                                  N                          0                                                                                      ⁢                                                                                                                    Y                          -                          HX                                                                                            2                                                        +                                                            ∑                                              j                        =                        1                                                                    TM                        c                                                              ⁢                                                                                            b                          j                                                ⁡                                                  (                          X                          )                                                                    ⁢                                                                        L                                                      a                            ,                            j                                                                          2                                                                                            )                                                                    ∑                                  X                  ∈                                      S                    -                    k                                                              ⁢                              exp                (                                                                            -                                              1                                                  N                          0                                                                                      ⁢                                                                                                                    Y                          -                          HX                                                                                            2                                                        +                                                            ∑                                              j                        =                        1                                                                    TM                        c                                                              ⁢                                                                                            b                          j                                                ⁡                                                  (                          X                          )                                                                    ⁢                                                                        L                                                      a                            ,                            j                                                                          2                                                                                            )                                                                        (        3        )            where bj(X)={±1} indicates the value of the j-th bit in the transmitted sequence X in binary antipodal notation.
Maximum A-posteriori Probability (MAP)—or also Maximum Likelihood (ML)—detection involves an exhaustive search over all the possible ST sequences of digitally modulated symbols: such a search becomes increasingly unfeasible with the growth of the spectral efficiency.
From equation (3) the following metric can be identified:
                              D          ⁡                      (            X            )                          =                                                            -                                  1                                      N                    0                                                              ⁢                                                                                      Y                    -                    HX                                                                    2                                      +                                          ∑                                  j                  =                  1                                                  TM                  c                                            ⁢                                                                    b                    j                                    ⁡                                      (                    X                    )                                                  ⁢                                                      L                                          a                      ,                      j                                                        2                                                              =                                    -                              D                ED                                      +                          D              a                                                          (        4        )            where DED is Euclidean distance (ED) term and Da is the a-priori term. The summation of exponentials involved in equation (4) is usually approximated according to the so-called “max-log” approximation:
                              ln          ⁢                                    ∑              x                        ⁢                          exp              ⁡                              [                                  D                  ⁡                                      (                    X                    )                                                  ]                                                    ≅                  ln          ⁢                                          ⁢                                    max              x                        ⁢                          exp              ⁡                              [                                  D                  ⁡                                      (                    X                    )                                                  ]                                                                        (        5        )            
Then equation (2) can be re-written as:
                              L                      p            ,            k                          ≅                                            max                              X                ∈                                  S                  +                  k                                                      ⁢                          D              ⁡                              (                X                )                                              -                                    max                              X                ∈                                  S                  -                  k                                                      ⁢                          D              ⁡                              (                X                )                                                                        (        6        )            corresponding to the so-called max-log-MAP detector. To conclude the description of the ideal detector, the a priori information La,k is subtracted, so that the detector outputs the extrinsic information Le,k to be passed to an outer decoder:Le,k=Lp,k−La,k  (7)
Because of their reduced complexity, sub-optimal linear detection procedures like Zero-Forcing (ZF) or Minimum Mean Square Error (MMSE) [9] are widely employed in wireless communications. To improve their performance, nonlinear detectors based on the combination of linear detectors and spatially ordered decision-feedback equalization (O-DFE) were proposed in [10]-[11]. There, the principles of interference cancellation and “layer” (i.e., antenna) ordering are established: accordingly, in the remainder of this document the terms “layer” and “antenna” will be used as synonymous.
The related systems suffer from performance degradation due to noise enhancements and error propagation; moreover, they are not suitable for soft-output generation.
More attractive for bit interleaved coded modulation (BICM) systems are soft interference cancellation (SIC) iterative MMSE and error correction decoding strategies [12]-[14]. They represent a suboptimal way to compute equations (2)-(3) where the ED term in (4) is replaced by linear MMSE filtering and interference cancellation. Unfortunately they suffer from latency and complexity disadvantages, and also their performance can be significantly improved, as shown in the present document.
Another important class of detectors is represented by the so-called list detectors [15]-[18]. These are based on a combination of the ML and DFE principles. The basic common idea exploited in list detectors (LD) is to divide the streams to be detected into two groups: first, one or more reference transmit streams are selected and a corresponding list of candidate constellation symbols is determined; then, for each sequence in the list, interference is cancelled from the received signal and the remaining symbol estimates are determined by as many sub-detectors operating on reduced size sub-channels. By searching all possible S cases for a reference layer, adopting O-DFE for the remaining T−1 sub-detectors, and utilizing a properly optimized layer ordering technique, a LD is able to maintain degradation within fractions of a dB in comparison with ML performance.
Notably, this can be accomplished through a parallel implementation. A drawback of this approach lies in that the computational complexity is high as T O-DFE detectors for T−1 sub-streams have to be computed. If efficiently implemented, it involves O(T4) complexity. Another major shortcoming of the prior work in list based detection is the absence of a procedure to produce soft bit metrics for use in coding and decoding procedures. For this reason, also Turbo or equivalently iterative SIC schemes have not been designed for LDs.
Another important family of ML-approaching detectors is based on lattice decoding procedures, applicable if the received signal can be represented as a lattice [19]-[20]. The so-called Sphere Decoder (SD) [25]-[26] is the most widely known example for these detectors and can be utilized to attain hard-output ML performance with significantly reduced complexity. However SD suffers from some important disadvantages, most notably, is not suitable for a parallel VLSI implementation; the number of lattice points to be searched is non-deterministic, sensitive to the channel and noise realizations, and to the initial radius. This is not desirable for real-time high-data rate applications. Finally, generation of soft output metrics is not easy with known lattice decoding procedures. As said for LDs, for this reason also Turbo or equivalently iterative SIC schemes have not been designed in conjunction with SD.
Besides performance (the benchmarks are optimal ML detection and linear MMSE, ZF on the two extremes, respectively) at least four basic features should be complied with by a MIMO detection arrangement in order to be effective and implementable in next generation wireless communication procedures:                high (i.e., optimal or near-optimal) performance;        reduced overall complexity;        the capability of generating bit soft output values, as this yields a significant performance gain in wireless systems employing error correction codes (ECC) coding and decoding procedures;        the capability of the architecture of the procedure to be parallelized, which is significant for an Application Specific Integrated Circuit (ASIC) implementation and also to yield the low latency required by a real-time high-data rate transmission.        